Ike, which photo are you referring to? I think the LCD is always folded over the top, not the back. Here is some of the text:
"The DSC-R1 has a really unique LCD monitor, mounted on the top of the camera it can flip-up and twist through 270 degrees. Usually it would be folded flat (as shown in the first image below), flip it up to enable LCD view and it can be used in a range of different positions. This also facilitates a fairly interesting waist-level 'medium format like' shooting option."
From what I saw the LCD can only be vertically (what would generate a lot of empty space in the housing), or flat on the top, what would be the "medium format like" postion, in which you would have to look down in order to shoot something in front of you. I don't think this is good for UW photography, unless you shoot a lot of over/under photos. Of course, you can always house it with the LCD closed and turned off, but the original post was referring to the advantage of having live preview on the LCD of the R1.